The main difference between the accelerometer array and gyroscope
state-space models is whether the angular velocity is propagated or
not in the navigation equations. In the
accelerometer array models, the accelerometer array measurements are the sole
input to the inertial navigation process and used both for calculating
the translational and rotational changes. Hence,
(REF ) to
() and
(REF ) to
() can be
used to realize a GFIMU inertial navigation
system [1]}, [2]}, [3]}, [4]}. The
accelerometer array models could thus be used for high dynamic
applications where gyroscopes usually saturate [5]}, [6]}. If
rotational information from gyroscopes are to be included this must be
done via some filtering framework, such as the Kalman filter. In that
case, (REF ) to
() and
(REF ) to
(), describe the system
dynamics and () and
() the
observation equation of the state-space model used in the filtering
process. A natural consequence of using the Kalman filter is that
accelerometer and gyroscope measurements
are fused using Kalman updates that have a fixed amount of
computations. This is not the case
for the current state-of-the-art method that fuses the
accelerometer and gyroscope measurements by solving a non linear optimization
problem using an iterative method [7]}. The Kalman updates will also
function as a feedback mechanism on \(\omega \) , which has the added
benefit of stabilizing
the potentially
unstable continuous-time equation
in (REF ) [3]}, [9]}.
Moreover, it is also
possible to fuse the gyroscope and
accelerometer array measurements for orientation estimation without
Kalman updates as shown
in the 2nd order gyroscope model. However, the gyroscope models will
not work when the gyroscopes saturate.
